Polar moment of inertia of a rectangular section

Orientation of a cross-section with respect to its bending axis is not crucial in obtaining a large moment of inertia. True False

Find the polar moment of inertia of a square section bar sized 3 1⁄2 in. x 3 1⁄2 in.

1. A circular disk has a density p(r) which varies as a function of distance from the center of the disk. The disk has a radius R and a thickness t. Assuming p(r) = Po(1-r/R): Calculate the total mass of the disk. a. b. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point G. C. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point O. G R

Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar. The dimensions of the section are: l=55 mm, h=22 mm The triangle: hT=12 mm, lT=19 mm and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 mm. A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? Enter the y position of the center of gravity of the bar in mm with one decimal.

Obtain the moment of inertia () of the flywheel from its dimensions (see figure below). Note that the flywheel is two cylinders of diameter 0.03086 m and one cylinder of diameter 0.2008 m. (For uniform cylinders, /= 1/2(MR2)) Since the masses are unknown, express the mass as the density (p) times the volume. Each part of the flywheel is made of the same material so there is only one density. You should now have an expression for the density in terms of I, the two diameters, the two thicknesses, and constants. 0.0520 m 0.03086 m 0.2008 m 0.0155 m

Find the moments of inertia of the shaded shape about the given centroidal x-axis (Ix) and centroidal y-axis (I). The equations for a single rectangle's moment of inertia about its own centroidal axis is given below. 4 h + y с A = bh Rectangular area X I₂ = 1/2bh³ bh³ Iy = 1 in 2 in 2 in y 1 in 2 in y' x' 2.375 in X

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The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment of inertia of the section about its base a-a. Assume b = 18 in., h = 5 in., r = 3 in, R = 5 in. Answer: la-a= i 2216.882 b R in.4 h